Ultrafast lasers generate a series of short optical pulses. Temporal separation of the pulses is determined by a round-trip time of light circulating in the resonant-cavity of the laser. If a high energy-per-pulse or high pulse-separation time is required, it is desirable to operate the laser with as long a resonant-cavity as possible.
Unfortunately, in many applications of ultrafast lasers, such as incorporating the laser in a small instrument, a laser having a cavity length of about 2 m or more is simply not practical. A practical length is about thirty centimeters (cm) or less. In certain applications, a length of 10 cm may be desirable. To "fold" a 2 m long cavity, using multiple reflections, in order to obtain a 10 cm longest physical dimension would require more than twenty reflections, accordingly minimizing reflection losses is important.
In most ultrafast lasers, a cavity loss in excess of 1.0% would lead to significant loss of output power. By way of example, in an ultrafast laser having 10% outcoupling, a 1% cavity loss (per round-trip) equates to about 10% loss of output power. Because of this, even if 99.9% reflecting fold-mirrors were used, more than about ten intra-cavity reflections therefrom per round-trip would produce significant output-power reduction.
Further, in order to support the ultrashort pulse length characteristic of an ultrafast laser, the laser must possess a total negative group-delay-dispersion, (negative GDD or NGDD) i.e., the sum of the GDD of the laser gain-medium and all cavity components must be negative. In a simple arrangement of a laser cavity and dielectric material therein, such as, a gain medium and a mode locking device, total cavity GDD would be positive, i.e., shorter wavelength light experiences a higher refractive index and lower group velocity, and lags behind longer wavelength light. This causes lengthening of a laser pulse each round trip and prevents stable, short-pulse operation.
One means of avoiding this is to include one or more NGDD devices having collective negative GDD at least equal to, and preferably greater than, this positive GDD. Furthermore, if the laser is to be tunable over a range of wavelengths, the NGDD devices must be effective over that range of wavelengths.
Reflective NGDD devices which have been used with prior-art ultrafast lasers include Gires-Tournois Interferometer (GTI) mirrors. A GTI-mirror is a multilayer NGDD-mirror including a reflector, which comprises a stack of alternating high and low refractive index dielectric layers, each layer generally having an optical thickness of one-quarter wavelength (one QWOT) at the nominal operating wavelength of the laser, and a single, thick, Fabry-Perot-like "spacer" layer (typically many wavelengths thick) of a dielectric material deposited on the reflector. A partially-reflecting multilayer stack may (optionally) be deposited on the spacer layer. A GTI-mirror typically gives a constant negative GDD over only a relatively narrow wavelength range, for example, about fifty nanometers (nm). In a GTI-mirror, the NGDD is achieved by selective resonant trapping of certain wavelengths in the spacer layer. Such a device is described extensively in a paper "Compression of Femto Second Optical Pulses with Dielectric Multilayer Interferometers", Kuhl et al., IEEE Transactions in Quantum Electronics, QE-22, 1, pp 182-185, (January 1986).
In U.S. Pat. No. 5,734,503 (Szipocs et al.) multilayer NGDD mirrors described as "chirped mirrors" are disclosed. One disclosed example of such a mirror includes a substrate having a structure of more than 40 layers deposited thereon. In this structure, essentially no two adjacent layers have the same optical thickness. Two materials are used for adjacent layers, one having a relatively high refractive index and the other a relatively low refractive index. Throughout the structure, the optical thickness between adjacent layers is substantial, with optical thickness ratios up to about 2:1 not being uncommon. The thickness of individual layers is computer generated (optimized) from an initial layer system described as "intuitive". Increasing individual layers in thickness from the front to the back of the layer system, i.e., from the outermost layer towards the substrate, or a fourier transform design is suggested, although no detail of such an initial layer system is disclosed.
It is taught that, following optimization, apart from a trend of increasing optical thickness of a "reflective period" from the front to the back of the layer system, the layer system does not have any orderly structure. It is taught that nearly-constant NGDD is achieved without the use of resonant trapping mechanisms in the structure, and results simply from different penetration depths of different wavelengths into the structure. Such a mirror appears to be able to provide constant NGDD over a broader band of wavelengths than a GTI-mirror, for example, up to about 150 nm, at a nominal center wavelength of about 800 nm, for a GDD of -45 fs.sup.2.
While the Szipocs et al. NGDD-mirror appears to achieve a desired value of nearly-constant NGDD over a bandwidth greater than has been achieved in devices of the GTI type which rely on a wide resonant-cavity to provide NGDD, it would appear from consideration of optical multilayer theory that the mirror structure is far from that which would produce the highest possible reflectivity over the broadest bandwidth with the same number of layers of the same materials.
It is well-known to designers of multilayer optical devices that the highest reflectivity that can be obtained with a group of layers having alternately high and low refractive index is achieved when all layers in the group have the essentially the same optical thickness (an optical thickness ratio of 1:1). Essentially, here meaning to the extent that is achievable considering refractive index dispersion in the materials. Departures from the 1:1 ratio will result in a lower reflectivity over a narrower bandwidth. The greater the departure the lower the reflectivity.
It would be advantageous to provide multilayer structures which achieved comparable NGDD to the Szipocs et al. structures over the same or broader bandwidth, while preserving sufficient order in the structures that the magnitude and bandwidth of reflectivity were not unduly compromised by any structural mechanisms or features necessary to provide that NGDD. The present invention provides such structures and methods for designing them.